Numerical Simulation of the Thermomechanical Behavior of Extruded Bismuth Telluride Alloy Module

Our research group developed over the past years a method to produce n- and p-type bismuth telluride alloys by mechanical alloying and powder extrusion. The resulting extruded rods possess a particular crystalline texture, which is advantageous for module fabrication processes but may have an impact on the stress distribution in modules under operating conditions. The reported mechanical strength of the extruded polycrystalline thermoelectric (TE) materials is larger than those of materials produced by directional solidification, allowing the fabrication of thinner TE modules in order to increase power densities. The stress arising from the resulting higher thermal gradients in thinner legs can eventually become greater than the TE material strength, which would limit further module thickness reduction. We present results of numerical simulations of TE modules behavior undertaken to evaluate the effect of leg lengths (1 mm, 500 mu m, and 250 mu m) on the stress level imposed by a given temperature difference that could cause their fracture. Different boundary conditions were imposed on the outer ceramic surfaces delimiting the module (e.g., both free or one anchored on a flat rigid surface). The boundary conditions and the mechanical strength of the soldering alloys are significant factors influencing the stress distribution in the TE alloy elements. We have also examined the effect of the crystalline texture of the extruded TE materials on the distribution and levels of stress, and found it to be marginal.